1. Chapter 5
Torsion

5. 5.5 Statically Indeterminate Torque-Loaded Members
Equilibrium equation:
TA + TB = T

6. Compatibility condition
Angle of twist of AC:
Angle of twist of CB:
Solution:

12. 5.6 Solid Noncircular Shafts (skip)
5.7 Thin-Walled Tubes Having Closed Cross-
Sections (skip)
5.8 Stress Concentration
* Stress concentration occurs at
(i) location where cross section changes, or
(ii) location where load is applied.

13. K – torsional stress
concentration factor
max is used for design

16. Chapter 6
Bending

17. 6.1 Shear and Moment Diagrams
Beam
Beam – slender bar, support transverse load

19. Internal Forces

20. * Normal force NB – perpendicular to cross-section
It tends to stretch or compress the member.
* Shear force VB – tangent (parallel) to cross-section
It tends to cut the member in transverse direction.
* Bending moment MB – couple moment
It tends to bend the member.

21. Sign Convention
* Distributed load
Upward - positive
* N – normal force
Tensile – positive
Compressive - negative
* V – shear force
Causing clockwise rotation – positive
* M – banding moment
Causing concave downward (hold water) – positive

22. Analysis Procedure
* Find support reactions.
* If concentrated forces exist, divide the beam into several
segments.
* Cut each segment in middle, draw FBD, write equilibrium
equations, and find shear force and moment.
* Draw shear and moment diagrams.
Note: Always draw internal forces in positive directions.
If the result is negative, the actual direction is opposite.

23. EXAMPLE 6.1

24. EXAMPLE 6.1 (CONTINUED)

27. EXAMPLE 6.3

29. EXAMPLE 6.4

30. EXAMPLE 6.4 (CONTINUED)

31. 6.2 Graphical Method for Constructing Shear and Moment Diagrams
Regions of Distributed Load
* Differential equations: